Casimir force dimensional analysis · CAP 2005 #5

Physics · modern-physics

Problem

Experiment shows that two perfectly neutral parallel metal plates separated by a small distance dd, attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, FF, depends only on the Planck constant hh, on the speed of light cc, and on dd. Which of the following has the best chance of being correct for FF? (a) F=hc/d2F = hc/d^2; (b) F=hc/d4F = hc/d^4; (c) F=hd2/cF = hd^2/c; (d) F=d4/hcF = d^4/hc.

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